Write down your R codes for full credit. Uniform(0, 1). Then set (a) Generate n =...

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Write down your R codes for full credit. Uniform(0, 1). Then set (a) Generate n = 100 data points as follows. Take X Yi Bo + beta₁ X₁ + €i, i = 1, 2,..., n, = where Bo = 3, B₁ = 5 and €; ~ N(0, 1). Plot the data. Fit the regression line. Add the fitted line to the plot. (b) Repeat the experiment in part (a) 1,000 times. You will get a different value of 3₁ each time. Denote these by (¹), ),..., (1000). What is the mean of these values? What do you expect the mean to be? Plot a histogram of 3(¹), (1000) (c) Repeat (b) but now take e; to have a Cauchy distribution. The Cauchy distribution looks like a Normal but it has very thick tails. How does the histogram change? Write down your R codes for full credit. Uniform(0, 1). Then set (a) Generate n = 100 data points as follows. Take X Yi Bo + beta₁ X₁ + €i, i = 1, 2,..., n, = where Bo = 3, B₁ = 5 and €; ~ N(0, 1). Plot the data. Fit the regression line. Add the fitted line to the plot. (b) Repeat the experiment in part (a) 1,000 times. You will get a different value of 3₁ each time. Denote these by (¹), ),..., (1000). What is the mean of these values? What do you expect the mean to be? Plot a histogram of 3(¹), (1000) (c) Repeat (b) but now take e; to have a Cauchy distribution. The Cauchy distribution looks like a Normal but it has very thick tails. How does the histogram change?

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